Current Electricity Ques 34
34. Two metal wires of identical dimension are connected in series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the metal wires respectively, the effective conductivity of the combination is :
[2015 RS]
(a) $\frac{\sigma_1+\sigma_2}{2 \sigma_1 \sigma_2}$
(b) $\frac{\sigma_1+\sigma_2}{\sigma_1 \sigma_2}$
(c) $\frac{\sigma_1 \sigma_2}{\sigma_1+\sigma_2}$
(d) $\frac{2 \sigma_1 \sigma_2}{\sigma_1+\sigma_2}$
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Answer:
Correct Answer: 34.(d)
Solution:
- (d) In figure, two metal wires of identical dimension are connected in series
$R _{eq}=\frac{l}{\sigma_1 A}+\frac{l}{\sigma_2 A}=\frac{l _{eq}}{\sigma _{eq} A _{eq}}$
$\frac{2 l}{\sigma _{eq} A}=\frac{l}{A}(\frac{\sigma_1+\sigma_2}{\sigma_1 \sigma_2})$
$\therefore \sigma _{eq}=\frac{2 \sigma_1 \sigma_2}{\sigma_1+\sigma_2}$
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